Related papers: Time delay for dispersive systems in quantum scatt…
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…
We propose a theory of the resonance-antiresonance scattering process which differs considerably from the classical one (the Breit-Wigner theory), which is commonly used in the phenomenological analysis. Here both resonances and…
We put forward a finite theory of quantum scattering of fundamental particles without using auxiliary particles. It suggests that to avoid ultraviolet divergencies and model faster-than-light effects it suffices to appropriately change only…
We consider the distribution of waiting times between non-interacting fermions on a tight-binding chain. We calculate the waiting time distribution for a quantum point contact and find a cross-over from Wigner-Dyson statistics at full…
We consider a multichannel wire with a disordered region of length $L$ and a reflecting boundary. The reflection of a wave of frequency $\omega$ is described by the scattering matrix $\mathcal{S}(\omega)$, encoding the probability…
In this paper, we study the dynamics and stability of a fundamental power system model when a time delay is imposed on the excitation of the generator. It is observed that sustained oscillations can arise in an otherwise stable power system…
We consider the classical map proposed previously to be the exact classical analogue of Rydberg Molecules calculated with the approximations relevant to the multi-channel quantum defect theory. The resulting classical map is analyzed at…
Time lags are ubiquitous in biophysiological processes and more generally in real-world complex networks. It has been recently proposed to use information-theoretic tools such as transfer entropy to detect and estimate a possible delay in…
This paper is concerned with the existence of traveling wave solutions for diffusive two-species Lotka-Volterra systems with delay in both the reaction and diffusion terms without monotonicity. We extend the partial or cross monotone…
The scattering of carriers by charged dislocations in semiconductors is studied within the framework of the linearized Boltzmann transport theory with an emphasis on examining consequences of the extreme anisotropy of the scattering…
We extend the recently proposed Time-Dependent Multi-Determinant approach (ref.[1]) to the description of fermionic propagators. The method hinges on equations of motions obtained using variational principles of Dirac type. In particular we…
We construct a time-dependent scattering theory for Schr\"odinger operators on a manifold $M$ with asymptotically conic structure. We use the two-space scattering theory formalism, and a reference operator on a space of the form $R\times…
A quantum scattering theory is developed for Fock states scattered by two-level systems in the free space. Compared to existing scattering theories that treat incident light semi-classically, the theory fully quantizes the incident light as…
Motivated by recent experiments, we consider a Schr\"{o}dinger cat superposition of two widely separated coherent states in thermal equilibrium. The time development of our system is obtained using Wigner distribution functions. In contrast…
We explore the usefulness of the existing relations between the $S$-matrix and time delay in characterizing baryon resonances in pion-nucleon scattering. We draw attention to the fact that the existence of a positive maximum in time delay…
Analytic solutions to the time-dependent Schr\"odinger equation for cutoff wave initial conditions are used to investigate the time evolution of the transmitted probability density for tunneling. For a broad range of values of the potential…
As an extension of the discrete Sommerfeld problems on lattices, the scattering of a time harmonic wave is considered on an infinite square lattice when there exists a pair of semi-infinite cracks or rigid constraints. Due to the presence…
The paper is devoted to a reaction-diffusion equation with delay arising in modelling the immune response. We prove the existence of travelling waves in the bistable case using the Leray-Schauder method. In difference with the previous…
In this article, we aim to study the scattering of the solution to the focusing inhomogeneous nonlinear Schr\"odinger equation with a potential of form \begin{align*} i\partial_t u+\Delta u- Vu=-|x|^{-b}|u|^{p-1}u \end{align*} in the energy…
We theoretically and experimentally establish a connection between linearly chirped pulse propagation properties and the complex generalization of Wigner-Smith time delay for both transmitted and reflected pulses in linear and dispersive…